Since the invention of the wave gear device by C. W. Musser (Patent Document 1) up to the present day, inventions for devices of various types have been conceived by its originator, as well as by numerous researchers, including the present inventor. Even limiting the discussion to inventions relating to the tooth profile, numerous different types have been proposed. For example, in Patent Document 2, the present inventor proposed using an involute tooth profile as a basic tooth profile; and in Patent Documents 3 and 4 proposed a tooth profile design method employing a procedure for approximating, by means of a rack, meshing of the teeth of a rigid internal gear and a flexible external gear of a wave gear device, to derive an addendum tooth profile that affords contact of the two gears over a wide area.
Typically, a wave gear device has a ring-shaped rigid internal gear, a flexible external gear disposed coaxially to the inside thereof, and a wave generator fitting inside thereof. The flexible external gear is provided with a flexible cylindrical barrel portion, a diaphragm radially extending from the rear end of this cylindrical barrel portion, and external teeth formed on the outside peripheral face section of the cylindrical barrel portion at the front end opening side thereof. The flexible external gear is flexed into ellipsoidal shape by the wave generator, and meshes with the rigid internal gear at both ends in the major axis direction of the ellipse.
The external teeth of the flexible external gear flexed into ellipsoidal shape have an increasing amount of flexure, proportional to the distance from the diaphragm, from the diaphragm side towards the front end opening along the tooth trace direction thereof. Moreover, sections of the tooth portion of the flexible external gear undergo repeated flexure in radial directions in association with rotation of the wave generator. However, to date, sufficient consideration has not been given to a rational method for establishing a tooth profile in a manner that takes into consideration such flexural action (coning) of the flexible external gear by the wave generator.
In Patent Document 5, the present inventor proposed a wave gear device provided with a tooth profile by which continuous meshing is possible, with consideration given to coning of the teeth. In the device proposed in Patent Document 5, an arbitrary axis-perpendicular cross section location in the tooth trace direction of the flexible external gear is selected as a principal cross section, and at a major axis position in an ellipsoidal rim neutral line of the flexible external gear in the principal cross section, an amount of flexure 2 κmn (where κ is the flexural coefficient, m is the module, and n is a positive integer) with respect to a rim neutral circle prior to flexure is established in such a way as to flex to a standard-deflection state of 2 mn (κ=1).
Additionally, using rack meshing to approximate meshing of the flexible external gear and the rigid internal gear, in axis-perpendicular cross sections at locations including the principal cross section in the tooth trace direction of the flexible external gear, movement loci of the teeth of the flexible external gear with respect to the teeth of the rigid internal gear in association with rotation of the wave generator are derived; a first homothetic curve BC is derived by scaling down, by a ratio λ (λ<1) while employing a point B as the homothetic center, a curve segment extending from a point A of an apical portion to the point B in the next bottom portion in a movement locus of a standard deflection obtained in the principal cross section, and this first homothetic curve BC is adopted as the basic tooth profile for the addendum of the rigid internal gear.
Furthermore, a second homothetic curve is derived by scaling, by a ratio (1−λ)/λ while employing an end point C of the first homothetic curve BC as the homothetic center, of a curve obtained by 180 degree rotation of the first homothetic curve BC about a center at the point C, and this second homothetic curve is adopted as the basic tooth profile for the addendum of the flexible external gear.
In addition to this, a transposition is applied to tooth profile sections to both sides, in the tooth trace direction, from the principal cross section in the tooth profile of the flexible external gear, doing so in such a way that both negative deflecting-side movement loci obtained in axis-perpendicular cross sections flexed to a negative deflection state (flexural coefficient λ<1) to the diaphragm side from the principal cross section in the external teeth of the flexible external gear, and positive deflection-side movement loci obtained in axis-perpendicular cross sections flexed to a positive deflection state (flexural coefficient λ>1) to the opening side from the principal cross section, describe curves that contact the bottom part of the standard-deflecting movement locus in the principal cross section. The resultant flexible external gear is a tapered flexible gear having an addendum circle of progressively smaller diameter from the opening side towards the diaphragm side in the tooth trace direction.
With a wave gear device in which such a tooth profile has been formed, centering on continuous meshing of tooth profile over a wide range in the principal cross section, effective meshing can be achieved in a tooth trace range extending to the opening end from the principal cross section, and in a tooth trace range extending to the diaphragm side from the principal cross section. Therefore, greater torque can be transmitted, as compared with a conventional wave gear device in which meshing takes place over a narrow tooth trace range.